We used \(8\times 7500\)  steps of the Adam stochastic optimizer [1]}
with a learning rate of \(\alpha = 10^{-3}\) . The variance parameter is
initialized at \(\sigma _{0} = 5\)  and the initial weights sample a normal
Gaussian. The grid is a \(15\times 15\)  node lattice with regularly spaced points
between \(-1, 1\)  and the elasticity parameter is \(\eta =1\) . During the first half
of the iterations, the “moons” data set from sci-kit [2]} learn is
sampled. Then, during the second half, the “circles” data set is sampled. Step
0 and each 7500 steps, data, weights and edges are plotted in
Fig. REF  from the upper left corner to the lower right one. We see that
the SOM tracks the changing data set, it correctly fits the observation density
(rather than its support as in [3]}) and it preserves the grid
neighborhood. In Fig. REF , the log standard deviation \(\sigma \)  and the
log distorsion (mean over the samples of the min squared distance with the
weights, cf [3]}) are plotted against time. Spikes appear half
time which means that the method detects the change in data and adapts
neighborhood radius accordingly.
